Surface phonons: Theoretical methods and results

Ab-initio methods; Bi(111); Density Functional Perturbation Theory; Electron-Phonon Interaction; Helium Atom Scattering; Lattice Dynamics; Multipole Expansion; Multipole Expansion Method; Surface Phonon Dispersion; Surface Vibrational Modes

Abstract :

[en] The theoretical methods currently in use for the calculation of surface phononsurface phonon dispersion curves and how they have evolved from the phenomenological force-constant models to the present day first principles theories are discussed. A selection of paradigmatic examples for the different classes of crystal surfaces is presented with comparisons to the experimental data obtained from helium atom scattering or electron energy-loss spectroscopy. © 2020, Springer Nature Switzerland AG.

Disciplines :

Physics

Author, co-author :

Benedek, G.; Department of Materials Science – U5, University of Milano-Bicocca, Milano, Italy, Donostia International Physics Center (DIPC), Donostia/San Sebastián, Spain

Bernasconi, M.; Department of Materials Science, University of Milano-Bicocca, Milano, Italy

Campi, D.; Theory and Simulation of Materials and National Centre for Computational Design and Discovery of Novel Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

Toennies, J. P.; Max-Planck-Institut fuer Dynamik und Selbstorganisation, Goettingen, Germany

Verstraete, Matthieu ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures

Language :

English

Title :

Surface phonons: Theoretical methods and results

Publication date :

2020

Journal title :

Springer Handbooks

ISSN :

2522-8692

Publisher :

Springer Science and Business Media Deutschland GmbH

Special issue title :

Surface Science

Pages :

737-782

Peer reviewed :

Peer reviewed

Available on ORBi :

since 11 February 2022

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Ioannes Duns Scotus (1265–1308): Physicorum Aristotelis Quaestiones, Tom. II, Lib. III–4 (L. Durand, Lyon 1639)
J.W. Strutt (Baron Rayleigh): On waves propagated along the plane surface of an elastic solid, Proc. Lond. Math. Soc. 17, 4 (1885)
J.W. Strutt (Baron Rayleigh): The Theory of Sound (MacMillan, London 1896), Reprinted by Dover, New York 1945
23.4 G. Benedek, J.P. Toennies: Atomic-Scale Dynamics at Surfaces – Theory and Experimental Studies with Helium Atom Scattering (Springer, Berlin, Heidelberg 2018), Chap. 3
23.5 G. Benedek, D. Campi, J.P. Toennies: Interaction of atoms with surfaces and surface phonons. In: Physics of Solid Surfaces, Subvol. A, Landolt Börnstein, New Ser., Subvol. 45A, ed. by P. Chiaradia, G.F. Chiarotti (Springer, Berlin, Heidelberg 2015) pp. 572–646, Chap. 10
H. Ibach: Surface vibrations of silicon detected by low-energy electron spectroscopy, Phys. Rev. Lett. 27, 253(1971)
23.7 B.R. Williams: Scattering of helium atoms by phonons in the (001) surface of LiF at 150 °K, J. Chem. Phys. 55, 3220(1971)
B.F. Mason, B.R. Williams: The inelastic scattering of He and Ne from a (001) surface of sodium fluoride, J. Chem. Phys. 61, 2765 (1974)
G. Boato, P. Cantini: Experiments on scattering of light atomic beams from crystal surfaces. In: Dynamics Aspects of Surface Physics, ed.by F.O. Goodman (Compositori, Bologna 1974) p. 707
23.10 P. Cantini, G.P. Felcher, R. Tatarek: Inelastic resonant transitions of atoms on a LiF surface, Phys. Rev. Lett. 37, 606(1976)
P. Cantini, P. Tatarek, G.P. Felcher: Selective adsorption in elastic and inelastic scattering of He and Ne from LiF(001) surface, Surf. Sci. 68, 104–112 (1977)
G. Benedek, G. Boato: Scattering of thermal atoms from crystal surfaces, Europhys. News 8(4), 5–8 (1977)
G. Boato, P. Cantini, R. Tatarek, S. Terreni: Atomic vibrations at the (0001) graphite surface studied by He atom scattering, Surf. Sci. 114, 485–497 (1982)
G. Boato, P. Cantini: Diffraction of neutral atoms and molecules from crystalline surfaces, Adv. Electron. Electron Phys. 60, 95–160 (1983)
J.M. Horne, D.R. Miller: Single-Rayleigh-phonon interaction in the scattering of He from LiF(001), Phys. Rev. Lett. 41, 511–514 (1978)
G. Brusdeylins, J.P. Toennies, H.-D. Meyer, K. Winkelmann: Production of helium nozzle beams with very high speed ratios. In: Rarefied gas dynamics; 10th Int. Symp., Aspen (American Institute of Aeronautics and Astronautics, New York 1977) pp. 1047–1059
G. Brusdeylins, R.B. Doak, J.P. Toennies: Observation of surface phonons in inelastic scattering of He atoms from LiF(001) crystal surfaces, Phys. Rev. Lett. 44, 1417(1980)
G. Brusdeylins, R.B. Doak, J.P. Toennies: Measurement of the dispersion relation for Rayleigh surface phonons of LiF(001) by inelastic scattering of He atoms, Phys. Rev. Lett. 46, 437(1981)
G. Brusdeylins, R.B. Doak, J.P. Toennies: Highresolution helium time-of-flight studies of Rayleigh surface-phonon dispersion curves of LiF, NaF, and KCl, Phys. Rev. B 27, 3662 (1983)
R.B. Doak, U. Harten, J.P. Toennies: Anomalous surface phonon dispersion relations for Ag(111) measured by inelastic scattering of He atoms, Phys. Rev. Lett. 51, 578(1983)
U. Harten, J.P. Toennies, C. Woll: Helium timeof-flight spectroscopy of surface-phonon dispersion curves of the noble metals, Faraday Discuss. Chem. Soc. 80, 137(1985)
B.F. Mason, B.R. Williams: Inelastic atom scattering from a Cu(001) surface and an ordered adsorbed layer of Xe atoms at 16 K, Phys. Rev. Lett. 46, 1138–1142 (1981)
B. Feuerbacher, R.F. Willis: Momentum transfer cutoff in the scattering of neon atoms from a nickel (111) surface, Phys. Rev. Lett. 526, 47–50 (1981)
J.P. Toennies: The study of the forces between atoms of single crystal surfaces from experimental phonon dispersion curves. In: Solvay Conf. Surf. Sci., Springer Ser. Surf. Sci., Vol. 14, ed. by F.W. de Wette (Springer, Berlin 1989) pp. 248–290
V. Bortolani, N.H. March, M.P. Tosi (Eds.): Interaction of Atoms and Molecules with Solid Surfaces (Plenum, New York 1990)
T.B. Grimley: Gas–surface interactions. In: Interaction of Atoms and Molecules with Solid Surfaces, ed. by V. Bortolani, N.H. March, M.P. Tosi (Plenum, New York 1990) pp. 25–52
W. Kohn: Theory of atom–surface collisions. In: Interaction of Atoms and Molecules with Solid Surfaces, ed. by V. Bortolani, N.H. March, M.P. Tosi (Plenum, New York 1990) pp. 53–70
H. Ibach: Surface vibration spectroscopy. In: Interaction of Atoms and Molecules with Solid Surfaces, ed. by V. Bortolani, N.H. March, M.P. Tosi (Plenum, New York 1990) pp. 325–356
F. García-Moliner: Basic vibrational properties of surfaces. In: Interaction of Atoms and Molecules with Solid Surfaces, ed. by V. Bortolani, N.H. March, M.P. Tosi (Plenum, New York 1990) pp. 71–116
C. Wöll: Phonons on surfaces: the importance of structure and adsorbates, Appl. Phys. A 53, 377– 387 (1991)
F.W. de Wette, W. Kress (Eds.): Surface Phonons, Springer Ser. Surf. Sci., Vol. 21 (Springer, Berlin, Heidelberg 1991)
J.P. Toennies: Experimental determination of surface phonons by helium atom and electron energy loss spectroscopy. In: Surface Phonons, ed. by F.W. de Wette, W. Kress (Springer, Berlin 1991) pp. 111–166
V. Celli: Theory of helium scattering from surface phonons. In: Surface Phonons, ed. by F.W. de Wette, W. Kress (Springer, Berlin 1991) pp. 167–192
R.B. Doak, D.J. Auerbach: Single phonon inelastic helium scattering. In: Atomic and Molecular Beam Methods, Vol. 2, ed. by G. Scoles, D.C. Laine, U. Valbusa (Oxford Univ. Press, New York 1992) p. 384
E. Hulpke (Ed.): Helium Atom Scattering from Surfaces (Springer, Berlin, Heidelberg 1992)
G. Benedek, J.P. Toennies: Helium atom scattering spectroscopy of surface phonons: genesis and achievements. In: Surface Science: The First Thirty Years, ed. by C.B. Duke (Elsevier, Amsterdam 1994)
G. Benedek, J.P. Toennies: Helium atom scattering spectroscopy of surface phonons: genesis and achievements, Surf. Sci. 299/300, 587–611 (1994)
23.38 G. Comsa: Surface scattering of thermal energy He beams: from the proof of the wave nature of atoms to a versatile and efficient surface probe, Surf. Sci. 299/300, 77(1994)
23.39 V. Celli: Interaction of atoms with surfaces. In: Physics of Solid Surfaces, Landolt-Börnstein, New Series III, Vol. 24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1995) p. 278, Part C
23.40 R.F. Wallis, S.Y. Tong: Surface phonons. In: Physics of Solid Surfaces, Landolt-Börnstein, New Series III, Vol. 24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1995) p. 434, Part B
F. Hofmann, J.P. Toennies: High-resolution helium atom time-of-flight spectroscopy of lowfrequency vibrations of adsorbates, Chem. Rev. 96, 1307 (1996)
23.42 M.C. Desjonquères, D. Spanjaard: Vibrations at surfaces. In: Concepts in Surface Physics (Springer, Berlin, Heidelberg 1996), Chap. 3
S.A. Safron: High-resolution helium atom scattering as a probe of surface vibrations. In: Advances in Chemical Physics, Vol. XCV, ed. by I. Prigogine, S.A. Rice (Wiley, New York 1996)
B. Gumhalter: Single-and multiphonon atom– surface scattering in the quantum regime, Phys. Rep. 351, 1 (2000)
G.D. Billing: Dynamics of Molecule Surface Interactions (Wiley, New York 2000)
M. Rocca: Surface phonon dispersion. In: Physics of Covered Surfaces, I. Adsorbate Layers on Surfaces, ed. by H.P. Bonzel (Springer, Heidelberg, Berlin 2002) pp. 1–68
J.R. Manson: Energy transfer to phonons in atom and molecule collisions with surfaces. In: Surface Dynamics, Vol. 3, ed. by W.N. Unertl (North Holland, Amsterdam 2006)
W. Widdra: Vibrations at surfaces. In: Surface and Interface Science, ed. by K. Wandelt (Wiley-VCH, Weinheim 2012) pp. 773–814
L. Vattuone, G. Bracco, M. Smerieri, L. Savio, M. Rocca: Supersonic molecular beams studies of surfaces. In: Dynamics of Gas–Surface Interactions, Springer Ser. Surf. Sci., Vol. 50, ed. by R. Díez Muiño, H. Busnengo (Springer, Berlin, Heidelberg 2013) pp. 1–23
R. Díez Muiño, H. Busnengo (Eds.): Dynamics of Gas–Surface Interactions (Springer, Berlin, Heidelberg 2013)
G.G. Rusina, E.V. Chulkov: Phonons on the clean metal surfaces and in adsorption structures, Russ. Chem. Rev. 82(6), 483–510 (2013)
M. DeKieviet, D. Dubbers, C. Schmidt, D. Scholz, U. Spinola:3He spin echo: new atomic beam technique for probing phenomena in the neV range, Phys. Rev. Lett. 75, 1919 (1995)
A.P. Jardine, S. Dworski, P. Fouquet, G. Alexandrowicz, D.J. Riley, G.Y.H. Lee, J. Ellis, W. Allison: Ultrahigh-resolution spin-echo measurement of surface potential energy landscapes, Science 304, 1790 (2004)
A.P. Jardine, H. Hedgeland, G. Alexandrowicz, W. Allison, J. Ellis: Helium-3 spin-echo: principles and application to dynamics at surfaces, Prog. Surf. Sci. 84, 323–379 (2009)
H. Ibach, D.L. Mills: Electron Energy Loss Spectroscopy and Surface Vibrations (Academic Press, New York 1982)
S. Lehwald, J.M. Szeftel, H. Ibach, T.S. Rahman, D.L. Mills: Surface phonon dispersion of Ni(100) measured by inelastic electron scattering, Phys. Rev. Lett. 50, 518 (1983)
X. Mu-Liang, B.M. Hall, S.Y. Tong, M. Rocca, H. Ibach, S. Lehwald, J.E. Black: Energy dependence of inelastic electron scattering cross section by surface vibrations: experimental measurement and theoretical interpretation, Phys. Rev. Lett. 54, 1171 (1985)
H. Ibach: Electron Energy Loss Spectrometers: The Technology of High Performance, Springer Ser. Opt. Sci., Vol. 63 (Springer, Berlin, Heidelberg 1991)
H. Ibach: Electron energy loss spectroscopy: the vibration spectroscopy of surfaces, Surf. Sci. 299/300, 116 (1994)
23.60 H. Ibach, M. Balden, S. Lehwald: Recent advances in electron energy loss spectroscopy of surface vibrations, J. Chem. Soc. Faraday Trans. 92, 4771– 4774 (1996)
23.61 H. Ibach: Physics of Surfaces and Interfaces (Springer, Berlin, Heidelberg 2007), Chap. 7
M. Rocca, H. Ibach, S. Lehwald, M.L. Xu, B.M. Hall, Y.S. Tong: Electron–phonon scattering and structure analysis. In: The Structure of Surfaces,ed.by M.A. van Hove, S.Y. Tong (Springer, Berlin, Heidelberg 1985) pp. 156–162
S. Lehwald, J.M. Szeftel, H. Ibach, T.S. Rahman, G.L. Mills: EELS study of the dynamics of clean Ni(100): surface phonons and surface resonances, Surf. Sci. 171, 632–642 (1986)
S. Lehwald, M. Rocca, H. Ibach, T.S. Rahman: Surface phonon dispersion of ordered overlayers, J. Electron Spectrosc. Relat. Phenom. 38, 29–44 (1986)
M. Rocca, H. Ibach, S. Lehwald, T.S. Rahman: Surface phonon dispersion of surface and adsorbate layers. In: Structure and Dynamics of Surfaces I, ed. by W. Schommers, P. von Blanckenhagen (Springer, Berlin, Heidelberg 1987) pp. 245–276
J.L. Erskine, E.-J. Jeong, J. Yater, Y. Chen, S.Y. Tong: Detection of odd symmetry shear modes at metal surfaces by inelastic electron scattering: experiment and theory, J. Vac. Sci. Technol. A 8, 2649 (1990)
Y. Chen, S.Y. Tong, M. Rocca, P. Moretto, U. Valbusa, K.H. Bohnen, K.M. Ho: High-resolution electron energy loss spectroscopy analysis of Ag(001): discovery of a new surface longitudinal mode using first-principles phonon calculations, Surf. Sci. 250, L389(1991)
Y. Chen, S.Y. Tong, J.S. Kim, L.L. Kesmodel, T. Rodach, K.P. Bohnen, K.M. Ho: Characterization of surface phonons on Cu(001) and Ag(001): firstprinciples phonon calculations with experimental and theoretical studies of high-resolution electron-energy-loss spectra, Phys. Rev. B 44, 11394 (1991)
M. Rocca, U. Valbusa: EELS cross-section of surface phonons on Ag(001), Nuovo Cim. 15D, 493–499 (1993)
23.70 L. Vattuone, M. Rocca, L. Savio: High resolution electron energy loss spectroscopy (HREELS): a sensitive and versatile surface tool. In: Surface Science Techniques, Springer Ser. Surf. Sci., Vol. 51, ed.byG.Bracco,B.Holst(Springer,Berlin,Heidelberg 2013) pp. 499–529, Chap. 17
M. Born, K. Huang: Dynamical Theory of Crystal Lattices (Clarendon, Oxford 1998)
A.A. Maradudin, E.W. Montroll, G.H. Weiss, I.P. Ipatova: Theory of Lattice Dynamics in the Harmonic Approximation, Solid State Physics, Suppl. 3 (Academic Press, New York 1971)
W. Cochran: The Dynamics of Atoms in Crystals (Arnold, London 1973)
P. Brüesch: Phonons: Theory and Experiments. Lattice Dynamics and Models of Interatomic Forces (Springer, Berlin, Heidelberg, New York 1982)
H. Böttger: Principle of the Theory of Lattice Dynamics (Akademie-Verlag, Berlin 1983), Sect. 1.4
M. Born, T. von Kármán: Über Schwingungen in Raumgittern, Phys. Z. 13, 297(1912)
R.F. Wallis: Effects of surfaces in lattice dynamics. In: Dynamical Properties of Solids, Vol.2,ed. by G.K. Horton, A.A. Maradudin (North-Holland, Amsterdam 1975) p. 443
J.E. Black: Surface phonons: metals. In: Dynamical Properties of Solids, Vol. 6, ed. by G.K. Horton, A.A. Maradudin (Elsevier, Amsterdam 1990) p. 179
R.E. Allen, G.P. Alldredge, F.W. de Wette: Surface modes of vibration in monatomic crystals, Phys. Rev. Lett. 23, 1285 (1969)
R.E. Allen, G.P. Alldredge, F.W. de Wette: Studies of vibrational surface modes, Phys. Rev. B 4, 1648–1661 (1971)
23.81 A.A. Maradudin, P. Mazur, E.W. Montroll, G.H. Weiss: Remarks on the vibrations of diatomic lattices, Rev. Mod. Phys. 30, 173(1958), App. A
L. Miglio, G. Benedek: Study of surface phonons by means of the Green’s function method. In: Structure and Dynamics of Surfaces II, ed. by W. Schommers, P. von Blanckenhagen (Springer, Berlin, Heidelberg 1987) p. 35
G. Benedek, L. Miglio: The Green’s function method in the surface lattice dynamics of ionic crystals. In: Surface Phonons, Springer Ser. Surf. Sci., Vol. 21, ed. by F.W. deWette, W. Kress (Springer, Berlin, Heidelberg 1991) pp. 37–66
G. Benedek: Surface lattice dynamics of ionic crystals by the Green function method, Phys. Status Solidi (b) 58, 661 (1973)
G. Benedek, G.P. Brivio, L. Miglio, V.R. Velasco: Dispersion relations of surface phonons in LiF(001) and NaF(001), Phys. Rev. B 26, 497 (1982)
S. Doniach, E.H. Sondheimer: Green’s Function for Solid State Physics (Benjamin, London 1974), Reprinted by Imperial College Press, London 1998
E.N. Economou: Green’s Function in Quantum Physics (Springer, Berlin, Heidelberg 1978)
23.88 I.M. Lifshitz, L.M. Rozenzweig: Dynamics of lattice filling half-space, Zh. Eksp. Teor. Fiz. 18, 1012 (1948), in Russian
I.M. Lifshitz, A.M. Kosevich: The dynamics of a crystal lattice with defects, Rep. Prog. Phys. 29(I), 217 (1966)
G. Benedek: Dynamics of solid surfaces, Phys. Mag. 7(suppl.), 1 (1985)
B.A. Lippmann, J. Schwinger: Variational principles for scattering processes, Phys. Rev. 79, 469 (1950)
G. Benedek: The Green function approach to the surface lattice dynamics of ionic crystals, Surf. Sci. 61, 603(1976)
L. van Hove: Correlations in space and time and born approximation scattering in systems of interacting particles, Phys. Rev. 95, 249(1954)
I.Y. Sklyadneva, G. Benedek, E.V. Chulkov, P.M. Echenique, R. Heid, K.-P. Bohnen, J.P. Toennies: Mode-selected electron–phonon coupling in superconducting Pb nanofilms determined from He atom scattering, Phys. Rev. Lett. 107, 095502 (2011)
G. Benedek, M. Bernasconi, K.-P. Bohnen, D. Campi, E.V. Chulkov, P.M. Echenique, R. Heid, I.Y. Sklyadneva, J.P. Toennies: Unveiling modeselected electron–phonon interactions in metal films by helium atom scattering, Phys. Chem. Chem. Phys. 16, 7159–7172(2014)
J.R. Manson, G. Benedek, S. Miret-Artès: Electron–phonon coupling strength at metal surfaces directly determined from the helium atom scattering Debye–Waller factor, J. Phys. Chem. Lett. 7, 1016–1021 (2016)
G. Benedek, S. Miret-Artès, J.P. Toennies, J.R. Manson: Electron–phonon coupling constant of metallic overlayers from specular He atom scattering, J. Phys. Chem. Lett. 9, 76–83(2018)
D. Campi, M. Bernasconi, G. Benedek, J.P. Toennies: Surface dynamics of Xe(111): an ambiguous nobility, J. Phys. Chem. C 119, 14579–14584 (2015)
B.M. Hall, D.L. Mills, M.H. Mohamed, L.L. Kesmodel: Surface lattice dynamics of Cu(111), Phys. Rev. B 38, 5856 (1988)
A. Šiber, B. Gumhalter, A.P. Graham, J.P. Toennies: He atom scattering and theoretical study of the surface phonons of a simple benchmark system: Xe(111), Phys. Rev. B 63, 115411 (2001)
E.W. Kellermann: Theory of the vibrations of the sodium chloride lattice, Philos. Trans. R. Soc. A 238, 513 (1940)
S.Y. Tong, A.A. Maradudin: Normal modes of a semi-infinite ionic crystal, Phys. Rev. 181, 1318 (1969)
L. Philippe, P. Lambin, P. Senet, A.A. Lucas: Phonon structure of thin films of the YBaCuO compound, Appl. Supercond. 2, 135(1994)
W. Cochran, R.A. Cowley: Phonons in perfect crystals. In: Encyclopedia of Physics 25/2a (Springer, Berlin, Heidelberg 1967) p. 83
23.105 J.R. Hardy: Phenomenological models in lattice dynamics. In: Dynamical Properties of Solids,Vol. 1, ed. by G.K. Horton, A.A. Maradudin (NorthHolland, Amsterdam 1974) p. 157, Chap. 3
23.106 H. Bilz, B. Gliss, W. Hanke: Title: Theory of phonons in ionic crystals. In: Dynamical Properties of Solids, Vol. 1, ed. by G.K. Horton, A.A. Maradudin (North-Holland, Amsterdam 1974) p. 343, Chap. 6
H. Bilz, W. Kress: Phonon Dispersion Relations in Insulators (Springer, Berlin, Heidelberg 1976)
B.C. Dick, A.W. Overhauser: Theory of the dielectric constants of alkali halide crystals, Phys. Rev. 112, 90 (1958)
W. Cochran: Theory of the lattice vibrations of germanium, Phys. Rev. Lett. 2, 495 (1959)
W. Cochran: Crystal stability and the theory of ferroelectricity, Adv. Phys. 9, 387(1960)
T.S. Chen, G.P. Alldredge, F.W. de Wette, R.E. Allen: Surface and pseudosurface modes in ionic crystal, Phys.Rev.Lett.26, 1543 (1971)
G.P. Alldredge: Shear-horizontal surface waves on the (001) face of cubic crystals, Phys. Lett. 41A,291 (1972)
T.S. Chen, G.P. Alldredge, F.W. de Wette, R.E. Allen: Surface modes of vibration in the rigid-Ion model of NaCl, Phys. Rev. B 6, 627(1972)
T.S. Chen, G.P. Alldredge, F.W. de Wette: Distribution of surface phonon branches in RbF and RbCl, Solid State Commun. 10, 941(1972)
T.S. Chen, G.P. Alldredge, F.W. de Wette: Surface phonons for the (001) face of lithium fluoride, Phys. Lett. 40 A, 401(1972)
V.L. Zoth, G.P. Alldredge, F.W. de Wette: On the existence of long-wavelength shear-horizontal surface waves on the bcc (001) surface, Phys. Lett. 47A, 247(1974)
T.S. Chen, F.W. de Wette, G.P. Alldredge: Studies of vibrational surface modes in ionic crystals. I. Detailed shell-model studies for the unrelaxed (001) face of seven crystals having the rocksalt structure, Phys. Rev. B 15, 1167 (1977)
G. Benedek, R.B. Doak, J.P. Toennies: Surfacephonon spectroscopy of LiF(001) by inelastic scattering of He atoms: theory and interpretation of time-of-flight spectra, Phys. Rev. B 28, 7277 (1983)
A.A. Lucas: Phonon modes of an ionic crystal slab, J. Chem. Phys. 48, 3156 (1968)
R. Fuchs, K.L. Kliever: Optical modes of vibration in an ionic crystal slab, Phys. Rev. 140, A2076 (1965)
A.D. Boardman (Ed.): Electromagnetic Surface Modes (Wiley, New York 1982)
G. Bracco, M. D’Avanzo, C. Salvo, R. Tatarek, F. Tommasini: Observation of acoustic and optical surface phonons in LiF(001) by inelastic He scattering, Surf. Sci. 189/190, 684(1987)
U. Schröder: A new model for lattice dynamics (“breathing shell model”), Solid State Commun. 4, 347(1966)
U. Schröder, V. Nüsslein: Calculations of dispersion curves and specific heat for LiF and NaCl using the breathing shell model, Phys. Status Solidi (b) 21, 309 (1967)
K. Fischer, H. Bilz, R. Haberkorn, W. Weber: Covalency and deformability of Ag+-ions in the lattice dynamics of silver halide, Phys. Status Solidi (b) 54, 285 (1972)
W. Kress, P. Roedhammer, H. Bilz, W.D. Teuchert, A.N. Christensen: Phonon anomalies in transition-metal nitrides: TiN, Phys. Rev. B 17, 111 (1978)
G. Benedek: Surface lattice dynamics. In: Dynamic Aspects of Surface Physics, ed. by F.O. Goodman (Compositori, Bologna 1974) p. 605
D. Eichenauer, J.P. Toennies: Theory of onephonon assisted adsorption and desorption of He atoms from a LiF(001) single crystal surface. In: Dynamics on Surfaces, ed. by B. Pullman, J. Jort ner, A. Nitzan, B. Gerber (Reidel, Dordrecht 1984) p. 1
W. Weber: Lattice dynamics of transition-metal carbides, Phys. Rev. B 8, 5082(1973)
23.130 A.N. Christensen, W. Kress, M. Miura, N. Lehner: Phonon anomalies in transition-metal nitrides: HfN, Phys. Rev. B 28, 977 (1983), and references therein
G. Benedek, M. Miura, W. Kress, H. Bilz: Anomalies in the surface–phonon dispersion of TiN(001), Phys. Rev. Lett. 52, 1907(1984)
G. Benedek, M. Miura, W. Kress, H. Bilz: Surface phonon anomalies in superconducting transition metal compounds, Surf. Sci. 148, 107(1984)
S.W. Musser, K.H. Rieder: Influence of surface force-constant changes on surface-mode frequencies, Phys. Rev. B 2, 3034 (1970)
K.H. Rieder, W. Drexel: Observation of vibrational surface modes in the acousto-optical bulk gap of TiN, Phys. Rev. Lett. 34, 148(1975)
E.B jr . Wilson, J.C. Decius, P.C. Cross: Molecular Vibrations (McGraw-Hill, New York 1955)
R. Tubino, L. Piseri, G. Zerbi: Lattice dynamics and spectroscopic properties by a valence force potential of diamondlike crystals: C, Si, Ge, and Sn, J. Chem. Phys. 6, 1022(1972)
P.N. Keating: First-and second-order dipole moments of homopolar crystals, Phys. Rev. 140A,369 (1965)
P.N. Keating: Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure, Phys. Rev. 145,637 (1966)
S.K. Sinha: Phonons in semiconductors, Crit. Rev. Solid State Sci. 3, 273(1973)
J.C. Phillips: Covalent bond in crystals. I. Elements of a structural theory, Phys. Rev. 166, 832(1968)
R.M. Martin: A simple bond charge model for vibrations in covalent crystals, Chem. Phys. Lett. 2, 268 (1968)
R.M. Martin: Dielectric screening model for lattice vibrations of diamond-structure crystals, Phys. Rev. 186, 871 (1969)
F.A. Johnson: A bond charge model of lattice dynamic, Proc. R. Soc. A 339, 73(1974)
W. Weber: New bond-charge model for the lattice dynamics of diamond-type semiconductors, Phys. Rev. Lett. 33, 371(1974)
K.C. Rustagi, W. Weber: Adiabatic bond charge model for the phonons in A3B5 semiconductor, Solid State Commun. 18, 637(1976)
W. Weber: Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α–Sn, Phys. Rev. B 15, 4789(1977)
A. Fleszar, R. Resta: Real-space force constants for lattice dynamics in silicon and germanium in the adiabatic bond-charge model, Phys. Rev. B 34, 7140 (1986)
L. Miglio, P. Santini, P. Ruggerone, G. Benedek: Dynamics of extensively reconstructed surfaces: Si(111) 2×1, Phys. Rev. Lett. 62, 3070 (1989)
P. Santini, L. Miglio, G. Benedek, U. Harten, P. Ruggerone, J.P. Toennies: Dynamics and structural assessment of open semiconductor surfaces: GaAs(110), Phys. Rev. B 42, 11942(1990)
G. Benedek, G. Onida: Bulk and surface dynamics of graphite with the bond charge model, Phys. Rev. B 47, 16471 (1993)
G. Benedek, F. Hoffmann, G. Onida, P. Ruggerone, L. Miglio: Surface phonons in layered crystals: theoretical aspects, Surf. Sci. Rep. 20, 3(1994)
M. Zitzlsperger, R. Honke, P. Pavone, U. Schröder: Ab initio calculation of the structure, the electronic states and the phonon dispersion of the Si(111)-(2×1) surface, Surf. Sci. 377, 108 (1997)
U. Harten, J.P. Toennies, C. Wöll: Observation of a 10-meV Einstein oscillator mode on the Si(111) (2×1) surface, Phys. Rev. Lett. 57, 2947(1986)
23.154 L. Wirtz, A. Rubio: The phonon dispersion of graphite revisited, Solid State Commun. 131, 141– 152 (2004)
J.L. Wilkes, R.E. Palmer, R.F. Willis: Phonons in graphite studied by EELS, J. Electron Spectrosc. Relat. Phenom. 44, 355(1987)
C. Oshima, T. Aizawa, R. Souda, Y. Ishizawa, Y. Sumiyoshi: Surface phonon dispersion curves of graphite (0001) over the entire energy region, Solid State Commun. 65, 1601 (1988)
C. Oshima, A. Nagashima: Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces, J. Phys. Condens. Matter 9, 1 (1997)
S. Siebentritt, R. Pues, K.-H. Rieder, A.M. Shikin: Surface phonon dispersion in graphite and in a lanthanum graphite intercalation compound, Phys. Rev. B 55, 7927 (1997)
M. Mohr, J. Maultzsch, E. Dobardžić, S. Reich, I. Milošević, M. Damnjanović, A. Bosak, M. Krisch, C. Thomsen: Phonon dispersion of graphite by inelastic x-ray scattering, Phys. Rev. B 76, 035439 (2007)
J. Maultzsch, S. Reich, C. Thomsen, H. Requardth, P. Ordejòn: Phonon dispersion in graphite, Phys. Rev. Lett. 92, 075501 (2004)
H. Yanagisawa, T. Tanaka, Y. Ishida, M. Matsue, E. Rokuta, S. Otani, C. Oshima: Analysis of phonons in graphene sheets by means of HREELS measurement and ab initiocalculation, Surf. Interface Anal. 37, 133(2005)
A. Grüneis, R. Saito, T. Kimura, L.C. Cancado, M.A. Pimienta, A. Jorio, A.G. Souza Filho, G. Dresselhaus, M.S. Dresselhaus: Determination of two-dimensional phonon dispersion relation of graphite by Raman spectroscopy, Phys. Rev. B 65, 155405 (2002)
R.J. Nemanich, G. Lucovsky, S.A. Solin: Optical probes of the lattice dynamics of graphite, Mater. Sci. Eng. 31, 157 (1977)
R. Nicklow, N. Wakabayashi, H.G. Smith: Lattice dynamics of pyrolytic graphite, Phys. Rev. B 5, 4951 (1972)
E. de Rouffignac, G.P. Alldredge, F.W. De Wette: Lattice dynamics of graphite slabs, Phys. Rev. B 23, 4208 (1981)
G.P. Alldredge, E. de Rouffignac, B. Firey, F.W. de Wette: Inadvertent symmetries in a lattice-dynamical model of graphite, Phys. Rev. B 29, 3712 (1984)
M. Maeda, Y. Kuramoto, C. Horie: Phonon dispersion relations of graphite, J. Phys. Soc. Jpn. Lett. 47, 337 (1979)
R. Al-Jishi, G. Dresselhaus: Lattice-dynamical model for graphite, Phys. Rev. B 26, 4514 (1982)
T. Aizawa, R. Souda, S. Otani, Y. Ishizawa, C. Oshima: Anomalous bond of monolayer graphite on transition-metal carbide surfaces, Phys. Rev. Lett. 64, 768(1990)
P.B. Allen: Charge-density distortions and lattice dynamics: a general theory and application to Nb, Phys.Rev.B16, 5139 (1977)
L.J. Sham: Electronic contribution to lattice dynamics in insulating crystal, Phys. Rev. 188, 1431 (1969)
R.M. Pick, M.H. Cohen, R.M. Martin: Microscopic theory of force constants in the adiabatic approximation, Phys. Rev. B 1, 910(1970)
R.M. Pick, M.H. Cohen, R.M. Martin: Microscopic theory of force constants in the adiabatic approximation, Phys. Rev. B 1, 910(1970)
W. Hanke: Microscopic theory of dielectric screening and lattice dynamics in the Wannier representation, Phys. Rev. B 8, 4585–4591 (1973)
L.J. Sham: Electronic influence on lattice dynamics. In: Elementary Excitations in Solids, Molecules, and Atoms, NATO Advanced Study Institute Series (Series B: Physics), Vol. 2, ed. by J.T. Devreese, A.B. Kunz, T.C. Collins (Springer, Boston, MA 1974) pp. 1–23
W. Hanke, L.J. Sham: Local-field and excitonic effects in the optical spectrum of a covalent crystal, Phys.Rev.B12, 4501 (1975)
W. Hanke, L.J. Sham: Many-particle effects in the optical spectrum of a semiconductor, Phys. Rev. B 21, 4656 (1980)
P.E. van Camp, V.E. van Doren, J.T. Devreese: Microscopic screening and phonon dispersion of silicon: moment expansion for the polarizability, Phys.Rev.Lett.42, 1224 (1979)
R. Resta, A. Baldereschi: Local-field effects and zone-center phonons in Si, Ge, GaAs, and ZnSe, Phys.Rev.B24, 4839(1981)
P.E. van Camp, V.E. van Doren, J.T. Devreese: Consistent microscopic calculation of phonons in Si, Phys.Rev.B25, 4270 (1982)
R. Resta: Local-field effects and phonon screening in polar semiconductors, Phys. Rev. B 27,3620 (1983)
P.E. van Camp, V.E. van Doren, J.T. Devreese: Ab initio phonon dispersion curves of Si, Phys. Rev. B 31, 4089(1985)
C. Falter: A unifying approach to lattice dynamical and electronic properties of solids, Phys. Rep. 164, 1(1988)
C.S. Jayanthi, H. Bilz, W. Kress, G. Benedek: Nature of surface-phonon anomalies in noble metals, Phys.Rev.Lett.59, 795(1987)
C. Kaden, P. Ruggerone, J.P. Toennies, G. Zhang, G. Benedek: Electronic pseudocharge model for the Cu(111) longitudinal-surface-phonon anomaly observed by helium-atom scattering, Phys.Rev.B46, 13509 (1992)
C. Kaden, P. Ruggerone, J.P. Toennies, G. Zhang, G. Benedek: Surface lattice dynamics and inelastic He scattering in Cu(111), Nuovo Cim. D 14, 627 (1992)
X. Zhu, Y. Yao, H.C. Hsu, F.C. Chou, M. ElBatanouny: Temperature-dependent anomalies in the structure of the (001) surface of LiCu2 O2, Surf. Sci. 605, 376 (2011)
X. Zhu, L. Santos, R. Sankar, S. Chikara, C. Howard, F.C. Chou, C. Charmon, M. El-Batanouny: Interaction of phonons and Dirac fermions on the surface of Bi2 Se3: a strong Kohn anomaly, Phys. Rev. Lett. 107, 186102 (2011)
X.T. Zhu, L. Santos, C. Howard, R. Sankar, F.C. Chou, C. Chamon, M. El-Batanouny: Electron–phonon coupling on the surface of the topological insulator Bi2 Se3 determined from surface–phonon dispersion measurements, Phys. Rev. Lett. 108, 185501 (2012)
R.G. Parr, W. Yang: Density Functional Theory of Atoms and Molecules (Oxford Univ. Press, New York 1989)
S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi: Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001)
E. Hulpke, J. Lüdecke: Hydrogen-induced phonon anomaly on the W(110) surface, Phys. Rev. Lett. 68, 2846 (1992)
E. Hulpke, J. Lüdecke: The giant surface phonon anomaly on hydrogen saturated W(110) and Mo(110), Surf. Sci. 287/288, 837 (1993)
G. Benedek, M. Bernasconi, V. Chis, E. Chulkov, P.M. Echenique, B. Hellsing, J.P. Toennies: Theory of surface phonons at metal surfaces: recent advances, J. Phys. Condens. Matter 22, 084020 (2010)
V. Bortolani, A. Franchini, F. Nizzoli, G. Santoro: Explanation of the anomalous peak observed in He-atom scattering from Ag(111), Phys. Rev. Lett. 52, 429(1984)
V. Bortolani, A. Franchini, G. Santoro: Santoro surface phonon calculations in metals and comparison with experimental techniques. In: Electronic Structure, Dynamics, and Quantum Structural Properties of Condensed Matter, ed. by J.T. Devreese, P. van Camp (Springer, Boston 1985) pp. 401–449
M.S. Daw, M.I. Baskes: Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals, Phys. Rev. Lett. 50, 1285 (1983)
M.S. Daw, M.I. Baskes: Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B 29, 6443(1984)
J.S. Nelson, E.C. Sowa, M.S. Daw: Calculation of phonons on the Cu(100) surface by the embedded-atom method, Phys. Rev. Lett. 61,1977(1988)
23.200 P.R. Underhill: An investigation of the anomalous surface phonon softening on noble metal (111) surfaces using the embedded atom method, Surf. Sci. 200, L441(1988)
N. Luo, W. Xu, S. Shen: Application of the embedded atom method to surface-phonon dispersions on Cu(100), Solid State Commun. 67, 837(1988)
M.S. Daw, S.M. Foiles, M.I. Baskes: The embedded-atom method: a review of theory and applications, Mater. Sci. Rep. 9, 251–310 (1993)
J.S. Nelson, M.S. Daw, E.C.S. Sowa: Embedded atom calculations of the Cu (001), (111), and (110) surface phonon spectra, Superlattices Microstruct. 7, 259(1990)
U. Harten, A.M. Lahee, J.P. Toennies, C. Wöll: Observation of a soliton reconstruction of Au(111) by high-resolution helium-atom diffraction, Phys. Rev. Lett. 54, 2619 (1985)
X.Q. Wang: Anomalous surface phonons of the reconstructed Au(111): a molecular-dynamics simulation, Phys. Rev. Lett. 67, 1294(1991)
E.M. McIntosh, P.R. Kole, M. El-Batanouny, D.M. Chisnall, J. Ellis, W. Allison: Measurement of the phason dispersion of misfit dislocations on the Au(111) surface, Phys. Rev. Lett. 110, 086103 (2013)
R. Ravelo, M. El-Batanouny: Molecular-dynamics study of the reconstructed Au(111) surface: low temperature, Phys. Rev. B 40, 9574 (1989)
G. Benedek, G. Lange, P. Ruggerone, J.P. Toennies: Lattice dynamics of the (7×7) reconstructed Si(111) surface from high-resolution helium atom scattering, Europhys. Lett. 41, 647 (1998)
I. Štich, K. Terakura, B.E. Larson: First-principles finite-temperature characterization of dynamics of the Si(111)-7×7, Phys. Rev. Lett. 74, 4491(1995)
I. Štich, J. Kohanoff, K. Terakura: Low-temperature atomic dynamics of the Si(111)-7×7, Phys. Rev. B 54, 2642 (1996)
I. Štich: First-principles finite-temperature simulation of surface dynamics: Si(111)-(7×7), Surf. Sci. 368, 152 (1996)
J. Kim, F.S. Khan, M. Yeh, J.W. Wilkins: Surface phonons of the Si(111)-7×7 reconstructed surface, Phys. Rev. B 52, 14709 (1995)
W. Harrison: Electronic Structure and the Properties of Solids (Dover, New York 1988)
Y.R. Wang, C.B. Duke: Rotational surface phonons on (110) cleavage surfaces of zincblende-structure compound semiconductors, Surf. Sci. 205, L755 (1988)
23.215 B. Sandfort, A. Mazur, J. Pollmann: Surface phonons of hydrogen-terminated semiconductor surfaces. I. The H:Si(111)-(1×1) surface, Phys. Rev. B 51, 7139 (1995)
A. Mazur, B. Sandfort, V. Gräschus, J. Pollmann: Phonons at hydrogen-terminated Si and diamond surfaces. In: Festkörperprobleme, Advances in Solid State Physics, Vol. 36, ed. by R. Helbig (Springer, Berlin, Heidelberg 1997) pp. 181–201
C.M. Varma, W. Weber: Phonon dispersion in transition metals, Phys. Rev. B 21, 6142 (1979)
23.218 W. Weber: First principles lattice dynamics of transition metals. In: The Electronic Structure of Complex Systems, NATO ASI Series (Series B: Physics), Vol. 113, ed. by P. Phariseau, W.M. Temmermann (Springer, Boston, MA 1984) pp. 345– 462
X.W. Wang, W. Weber: Surface-phonon instabilities of W(001), Phys. Rev. Lett. 58, 1452(1987)
X.W. Wang, C.T. Chan, K.-H. Ho, W. Weber: Role of surface-state nesting in the incommensurate reconstruction of Mo(001), Phys. Rev. Lett. 60, 2066 (1988)
F. Mauri, G. Galli, R. Car: Orbital formulation for electronic-structure calculations with linear system-size scaling, Phys. Rev. B 47, 9973 (1993)
P. Ordejòn, D. Drabold, M. Grunbach, R. Martin: Unconstrained minimization approach for electronic computations that scales linearly with system size, Phys. Rev. B 48, 14646 (1993)
S. Goedecker, L. Colombo: Efficient linear scaling algorithm for tight-binding molecular dynamics, Phys. Rev. Lett. 74, 122(1994)
S. Goedecker: Linear scaling electronic structure methods, Rev. Mod. Phys. 71, 1085 (1999)
L. Colombo, M. Rosati: Parallel tight-binding molecular dynamics simulations on symmetric multi-processing platforms, Comput. Phys. Commun. 128, 108 (2000)
S. Nelson, M.S. Daw, E.C. Sowa: Cu(111) and Ag(111) surface-phonon spectrum: the importance of avoided crossings, Phys. Rev. B 40, 1465(1989)
M.H. Mohamed, L.L. Kesmodel, B.M. Hall, D.L. Mills: Surface phonon dispersion on Cu(111), Phys. Rev. B 37, 2763(1988)
L.J. Sham: A calculation of the phonon frequencies in sodium, Proc. R. Soc. A 283, 33 (1965)
W. Harrison: Pseudopotentials in the Theory of Metals (Benjamin, New York 1966)
A.O.E. Animalu, F. Bonsignori, V. Bortolani: The phonon spectra of alkali metals and aluminium, Nuovo Cim. B 44, 159(1966)
23.231 E.G. Brovman, Y.M. Kagan: Dlinnovolnovye fonony v metallakh, Zh. Eksp. Teor. Fiz. 57, 1329 (1970), Engl. Transl.: Long-wave phonons in metals, Sov. Phys. JETP 30:721 (1970)
23.232 E.G. Brovman, Y.M. Kagan: Phonons in nontransition metals, Soviet Physics Uspekhi 17, 125–152 (1974), Translated from Usp. Fiz. Nauk 112, 369–426 (1974)
C. Beatrice, C. Calandra: Surface screening effects in the vibrational spectra of simple metal surfaces, Phys. Rev. B 10, 6130 (1983)
C. Calandra, A. Catellani, C. Beatrice: Surface vibrations of Na(001) and K(001) surfaces, Surf. Sci. 148, 90(1984)
23.235 C. Calandra, A. Catellani, C. Beatrice: Pseudopotential theory of the vibrational properties of simple metal surfaces, Surf. Sci. 152/153,814(1985)
A.G. Eguiluz: Dynamical density response function of a metal-film in the random-phase approximation, Phys. Rev. Lett. 51, 1097(1983)
A.G. Eguiluz: Self-consistent static-density-response function of a metal surface in densityfunctional theory, Phys. Rev. B 31, 3303 (1985)
A.G. Eguiluz: Electronic screening at the surface of an sp-bonded metal, Phys. Scr. 36, 651 (1987)
J.A. Gaspar, A.G. Eguiluz, M. Gester, A. Lock, J.P. Toennies: Resonances in the surface-phonon spectrum of an sp-bonded metal, Phys. Rev. Lett. 66, 337 (1991)
W.A. Harrison: Transition-metal pseudopotentials, Phys. Rev. 181, 1036 (1969)
J.A. Moriarty: Density-functional formulation of the generalized pseudopotential theory. II, Phys. Rev. B 26, 1754(1982)
W. Kohn, L.J. Sham: Self-consistent equations including exchange and correlation effect, Phys. Rev. A 140, 1133 (1965)
Z.D. Popovic, M.J. Stott: Nonlinear, self-consistent theory of proton screening in metals applied to hydrogen in Al and Mg, Phys. Rev. Lett. 33, 1164 (1974)
E. Zaremba, W. Kohn: Theory of helium adsorption on simple and noble-metal surfaces, Phys. Rev. B 15, 12769(1977)
E. Zaremba, L.M. Sander, H.B. Shore, J.H. Rose: Self-consistent screening of a proton in jellium, J. Phys. F 7, 1763(1977)
M.D. Whitmore: Helium heat of solution in Al and Mg using non-linear self-consistent screening of the nucleus, J. Phys. F 6, 1259(1976)
J.K. Nørskov: Electronic structure of H and He in metal vacancies, Solid State Commun. 24, 691 (1977)
D.S. Larsen, J.K. Nørskov: Calculated energies and geometries for hydrogen impurities in Al and Mg, J. Phys. F 9, 1975(1980)
J.K. Nørskov, N.D. Lang: Effective-medium theory of chemical binding: application to chemisorption, Phys. Rev. B 21, 2131 (1980)
M.J. Stott, E. Zaremba: A model for light impurities in metals, Solid State Commun. 32, 1297(1979)
M.J. Stott, E. Zaremba: Quasiatoms: an approach to atoms in nonuniform electronic system, Phys. Rev. B 22, 1564 (1980)
A.E. Carlsson: Beyond pair potentials in elemental transition metals and semiconductors. In: Solid State Physics, Vol.43,ed.byH.Ehrenreich, D. Turnbull (Academic Press, Boston 1990) pp. 1–91
W.K. Jacobsen, J.K. Nørskov, M.J. Puska: Interatomic interactions in the effective-medium theory, Phys. Rev. B 35, 7423(1987)
23.254 P.D. Ditlevsen, J.K. Nørskov: The surface phonons of Cu(111), J. Electron Spectrosc. Relat. Phenom. 54/55, 237(1990)
P.D. Ditlevsen, J.K. Nørskov: Vibrational properties of aluminum, nickel and copper surfaces, Surf. Sci. 254, 261(1991)
M.W. Finnis, J.E. Sinclair: A simple empirical Nbody potential for transition metals, Philos. Mag. A 50, 45(1984)
V. Rosato, M. Guillope, B. Legrand: Thermodynamical and structural properties of f.c.c. transi tion metals using a simple tight-binding model, Philos. Mag. A 59(2), 321 (1989)
J. Guevara, A.M. Llois, M. Weismann: Model potential based on tight-binding total-energy calculations for transition-metal systems, Phys. Rev. B 52, 11509 (1995)
F. Raouafi, C. Barreteau, M.C. Desjonquères, D. Spanjaard: The phonon spectra of low and high index surfaces of copper, Surf. Sci. 507,748(2002)
F. Ercolessi, E. Tosatti, M. Parrinello: Au(100) reconstruction in the glue model, Surf. Sci. 177, 314 (1986)
F. Ercolessi, M. Parrinello, E. Tosatti: Simulation of gold in the glue model, Philos. Mag. A 58, 513 (1988)
X.Q. Wang, G.L. Chiarotti, F. Ercolessi, E. Tosatti: Anomalous high-frequency modes of “missingrow” reconstructed (110) surfaces, Phys. Rev. B 38, 8131 (1988)
J.R. Smith, A. Banerjea: New approach to calculation of total energies of solids with defects: surface-energy anisotropies, Phys. Rev. Lett. 59, 2451 (1987)
I.Y. Sklyadneva, G.G. Rusina, E.V. Chulkov: Vibrational states on vicinal surfaces of Al, Ag, Cu and Pd, Surf. Sci. 416, 17 (1998)
G. Witte, J. Braun, A. Lock, J.P. Toennies: Heliumatom-scattering study of the dispersion curves of step-localized phonons on Cu(211) and Cu(511), Phys.Rev.B52, 2165 (1995)
P. Hohenberg, W. Kohn: Inhomogeneous electron gas, Phys. Rev. 136, 864(1964)
E.K.U. Gross, R.M. Dreizler (Eds.): Density Functional Theory (Plenum, New York 1994)
R.M. Martin: Electronic Structure: Basic Theory and Pratical Methods (Cambridge Univ. Press, Cambridge 2004)
J.P. Perdew, A. Zunger: Self-interaction correction to density-functional approximations for manyelectron systems, Phys. Rev. B 23, 5048(1981)
A.D. Becke: Density-functional exchange-energy approximation with correct asymptotic behavior, Phys.Rev.A38, 3098 (1988)
J.P. Perdew: Unified theory of exchange and correlation beyond the local density approximation. In: Electronic Structure of Solids, ed. by P. Ziesche, H. Eschrig (Akademie, Berlin 1991) pp. 11–20
J.P. Perdew, K. Burke, M. Ernzerhof: Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865(1996)
R. Car, M. Parrinello: Unified approach for molecular dynamics and density-functional theory, Phys.Rev.Lett.55, 2471(1985)
23.274 A. Ancilotto, W. Andreoni, A. Selloni, R. Car, M. Parinello: Surface phonons from ab-initio molecular dynamics: Si(111) 2×1. In: Phonons 89, ed. by S. Hunklinger, W. Ludwig, G. Weiss (World Scientific, Singapore 1990) p. 931
F. Ancillotto, W. Andreoni, A. Selloni, R. Car, M. Parrinello: Structural, electronic, and vibrational properties of Si(111)-2×1 from ab initio molecular dynamics, Phys. Rev. Lett. 65, 3148 (1990)
R. di Felice, A.I. Shkrebtii, F. Finocchi, C.M. Bertoni, G. Onida: Surface vibrations at clean and hydrogenated GaAs(110) from ab-initio molecular dynamics, J. Electron Spectrosc. Relat. Phenom. 64/65, 697 (1993)
O.F. Sankey, D.J. Niklewski: Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems, Phys. Rev. B 40, 3979(1989)
J. Harris: Simplified method for calculating the energy of weakly interacting fragments, Phys. Rev. B 31, 1770(1985)
D.R. Alfonso, D.A. Drabold, S.E. Ulloa: Phonon modes of diamond (100) surfaces from ab initio calculations, Phys. Rev. B 51, 1989(1995)
D.R. Alfonso, D.A. Drabold, S.E. Ulloa: Structural, electronic, and vibrational properties of diamond (100), (111), and (110) surfaces from ab initio calculation, Phys. Rev. B 51, 14669(1995)
V. Heine, D. Weaire: Pseudopotential theory of cohesion and structure. In: Solid State Physics, Vol. 24, ed. by H. Ehrenreich, F. Seitz, T. Turnbull (Academic Press, New York 1970) pp. 249–463
H. Wendel, R.M. Martin: Theory of structural properties of covalent semiconductors, Phys. Rev. B 19, 5251(1979)
K. Kunc, R.M. Martin: Density-functional calculation of static and dynamic properties of GaAs, Phys. Rev. B 24, 2311(1981)
M.T. Yin, M.L. Cohen: Theory of lattice-dynamical properties of solids: application to Si and Ge, Phys. Rev. B 26, 3259 (1982)
K.M. Ho, C.L. Fu, B.N. Harmon, W. Weber, D.R. Hamann: Vibrational frequencies and structural properties of transition metals via totalenergy calculations, Phys. Rev. Lett. 49,673(1982)
K.-P. Bohnen, A. Eichler, J. Hafner: First principles calculations of surface phonons on Rh(111), Surf. Sci. 368, 222 (1996)
G. Witte, J.P. Toennies, C. Woll: Comparison of surface phonon dispersion curves for clean and hydrogen covered Rh(111) surfaces, Surf. Sci. 323, 228 (1995)
J. Friedel: Metallic alloys, Nuovo Cim. 7, 287 (1958)
W.A. Harrison: Solid State Theory (Dover, New York 1979), Chap. II
W. Li, J. Carete, N.A. Katcho, N. Mingo: ShengBTE: a solver of the Boltzmann transport equation for phonons, Comput. Phys. Commun. 185,1747(2014)
A. Togo, I. Tanaka: First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015)
P. Souvatzis, D. Legut, O. Eriksson, K.I. Katsnelson: Ab initio study of interacting lattice vibrations and stabilization of the β-phase in Ni-Ti shapememory alloy, Phys. Rev. B 81, 092201 (2010)
O. Hellman, I.A. Abrikosov, S.I. Simak: Lattice dynamics of anharmonic solids from first principles, Phys. Rev. B 84, 180301(R) (2011)
I. Errea, M. Calandra, F. Mauri: First-principles theory of anharmonicity and the inverse isotope effect in superconducting palladium-hy dride compounds, Phys. Rev. Lett. 111, 177002 (2013)
K.M. Ho, K.P. Bohnen: First-principles calculation of surface phonons on the Al(110) surface, Phys. Rev. Lett. 56, 934(1986)
K.M. Ho, K.P. Bohnen: Surface-phonon calculations for the Al(110) surface, Phys. Rev. B 38, 12897 (1988)
K.P. Bohnen, K.M. Ho: First principles calculation of lattice relaxation and surface phonons on Al(100), Surf. Sci. 207, 105(1988)
K.P. Bohnen, K.M. Ho: Structure and dynamics at metal surfaces, Surf. Sci. Rep. 19, 99 (1993)
R. Heid, K.-P. Bohnen: Ab initio lattice dynamics of metal surfaces, Phys. Rep. 387, 151 (2003)
T. Rodach, K.P. Bohnen, K.M. Ho: First-principles study of the Na(110) surface, Surf. Sci. 209, 481 (1989)
A.M. Lahee, J.P. Toennies, C. Wöll, K.P. Bohnen, K.M. Ho: Comparison of helium atom scattering surface phonon dispersion curves of the (1×2) reconstructed Au(110) surface with first-principle calculations, Europhys. Lett. 10, 261(1989)
23.302 T. Rodach, K.P. Bohnen, K.M. Ho: First principles calculations of lattice relaxation at low index surfaces of Cu, Surf. Sci. 286, 66 (1993)
T. Rodach, K.P. Bohnen, K.M. Ho: First principles calculations of surface phonons for Cu(110), Surf. Sci. 296, 123 (1993)
23.304 A.E. Eguiluz, A.A. Quong: Electronic screening in metals: from phonons to plasmons. In: Dynamical Properties of Solids, Vol.7,ed.byG.K.Horton, A.A. Maradudin (North-Holland, Amsterdam 1995) pp. 425–507, Chap. 6
A.A. Quong, B.M. Klein: Self-consistent-screening calculation of interatomic force constants and phonon dispersion curves from first principles, Phys. Rev. B 46, 10734 (1992)
A.A. Quong, A.G. Eguiluz: First-principles evaluation of dynamical response and plasmon dispersion in metals, Phys. Rev. Lett. 70, 3955 (1993)
R.F. Wallis, A.A. Maradudin, V. Bortolani, A.G. Eguiluz, A.A. Quong, A. Franchini, G. Santoro: Comparison between phenomenological and pseudopotential force constants for the lattice dynamics of Al, Phys. Rev. B 48, 6043 (1993)
A.A. Quong: First-principles determination of the interatomic-force-constant tensor of Au, Phys. Rev. B 49, 3226 (1994)
M. Buongiorno Nardelli, S. Baroni, P. Giannozzi: Phonon softening and high-pressure low-symmetry phases of cesium iodide, Phys. Rev. Lett. 69, 1069 (1992)
P. Giannozzi, S. de Gironcoli, P. Pavone, S. Baroni: Ab initio calculation of phonon dispersions in semiconductors, Phys. Rev. B 43, 7231 (1993)
J. Xie, S. de Gironcoli, S. Baroni, M. Scheffler: Temperature-dependent surface relaxations of Ag(111), Phys. Rev. B 59, 970 (1999)
23.312 A. dal Corso, A. Pasquarello, A. Baldereschi: Density-functional perturbation theory for lattice dy namics with ultrasoft pseudopotentials, Phys. Rev. B 56, R11369 (1997)
A. dal Corso: Density-functional perturbation theory with ultrasoft pseudopotentials, Phys. Rev. B 64, 235118 (2001)
S. Baroni, P. Giannozzi, A. Testa: Green’s-function approach to linear response in solids, Phys. Rev. Lett. 58, 1861(1987)
X. Gonze: Perturbation expansion of variational principles at arbitrary order, Phys. Rev. A 52, 1086 (1995)
X. Gonze: Adiabatic density-functional perturbation theory, Phys. Rev. A 52, 1096(1995)
S. de Gironcoli: Lattice dynamics of metals from density-functional perturbation theory, Phys. Rev. B 51, 6773 (1995)
W.E. Pickett: Pseudopotential methods in condensed matter applications, Comput. Phys. Rep. 9, 115(1989)
M.C. Payne, M.P. Teter, D.C. Allen, T.A. Arias, J.D. Joannopoulos: Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients, Rev. Mod. Phys. 64, 1045 (1992)
D.R. Hamann, M. Schluter, C. Chiang: Norm-conserving pseudopotentials, Phys. Rev. Lett. 43,1494 (1979)
L. Kleinman, D.M. Bylander: Efficacious form for model pseudopotentials, Phys. Rev. Lett. 48,1425 (1982)
D. Vanderbilt: Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41, 7892(1990)
X. Gonze, J.-M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.-M. Rignanese, L. Sindic, M. Verstraete, G. Zerah, F. Jollet, M. Torrent, A. Roy, M. Mikami, P. Ghosez, J.-Y. Raty, D.C. Allan: Firstprinciples computation of material properties: the ABINIT software project, Comput. Mater. Sci. 25, 478(2002)
X. Gonze, G.-M. Rignanese, M. Verstraete, J.-M. Beuken, Y. Pouillon, R. Caracas, F. Jollet, M. Torrent, G. Zerah, M. Mikami, P. Ghosez, M. Veithen, J.-Y. Raty, V. Olevano, F. Bruneval, L. Reining, R.W. Godby, G. Onida, D.R. Hamann, D.C. Allan: A brief introduction to the ABINIT software package, Z. Kristallogr. 220, 558 (2005)
A. Dal Corso, A. Mosca Conte: Spin-orbit coupling with ultrasoft pseudopotentials: application to Au andPt,Phys.Rev.B71, 115106 (2005)
A. Dal Corso: Density functional perturbation theory for lattice dynamics with fully relativistic ultrasoft pseudopotentials: application to fcc-Pt and fcc-Au, Phys. Rev. B 76, 054308 (2007)
M.J. Verstraete, M. Torrent, F. Jollet, G. Zérah, X. Gonze: Density functional perturbation theory with spin-orbit coupling: phonon band structure of lead, Phys. Rev. B 78, 045119 (2008)
A. Dal Corso: Ab initio phonon dispersions of face centered cubic Pb: effects of spin–orbit coupling, J. Phys. Condens. Matter 20, 445202 (2008)
S.Y. Savrasov, O.K. Andersen: Linear-response calculation of the electron–phonon coupling in doped CaCuO2, Phys. Rev. Lett. 77, 4430(1996)
R. Yu, H. Krakauer: Linear-response calculations within the linearized augmented plane-wave method, Phys. Rev. B 49, 4467(1994)
R. Kouba, A. Taga, C. Ambrosch-Draxl, L. Nordström, B. Johansson: Phonons and electron– phonon interaction by linear-response theory within the LAPW method, Phys. Rev. B 64, 184306 (2001)
J. K. Dewhurst, S. Sharma, L. Nordström, F. Cricchio, O. Grånäs, E. K. U. Gross: The Elk Code Manual. Version 5.3.25, http://elk.sourceforge.net
M. Dion, H. Rydberg, E. Schroeder, D.C. Langreth, B.I. Lundquist: Van der Waals density functional for general geometries, Phys. Rev. Lett. 92, 246401 (2004)
K. Lee, E.D. Murray, L. Kong, B.I. Lundquist, D.C. Langreth: Higher-accuracy van der Waals density functional, Phys. Rev. B 82, 081101 (2010)
V. Cooper: Van der Waals density functional: an appropriate exchange functional, Phys. Rev. B 81, 161104 (2010)
S. Grimme, J. Antony, S. Ehrlich, S. Krieg: A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010)
T. Thonhauser, S. Zuluaga, C.A. Arter, K. Berland, E. Schröder, P. Hyldgaard: Spin signature of nonlocal correlation binding in metal–organic frameworks,Phys.Rev.Lett.115, 136402(2015)
S. Azadi, R.E. Cohen: Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo, J. Chem. Phys. 145, 064501 (2016)
P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch: QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter 21, 395502 (2009)
X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D.R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M.J.T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.-M. Rignanese, D.Sangalli,R.Shaltaf,M.Torrent,M.J.Verstraete, G. Zerah, J.W. Zwanziger: ABINIT: first-principles approach to material and nanosystem properties, Comput. Phys. Commun. 180, 2852 (2009)
23.341 G. Kresse, J. Furtmüller: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996)
S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Probert, K. Refson, M.C. Payne: First principles methods using CASTEP, Z. Kristallogr. 220(5/6), 567 (2005)
D. Campi, M. Bernasconi, G. Benedek, A.P. Graham, J.P. Toennies: Surface lattice dynamics and electron–phonon interaction in cesium ultrathin films, Phys. Chem. Chem. Phys. 19, 16358 (2017)
E. Hulpke, J. Lower, A. Reichmuth: Strain and confined resonances in ultrathin alkali-metal films, Phys. Rev. B 53, 13901(1996)
A. Politano, G. Chiarello, G. Benedek, E.V. Chulkov, P.M. Echenique: Vibrational spectroscopy and theory of alkali metal adsorption and co-adsorption on single-crystal surfaces, Surf. Sci. Rep. 68, 305–389 (2013)
S. Andersson, J.P. Pendry, P.M. Echenique: Low energy electron diffraction from Na(110) and Na2O(111) surface, Surf. Sci. 65, 539(1977)
G. Benedek, J.P. Toennies: Systematic trends in the normal enhancement of the phonon anharmonicity at the surface of metals, Phys. Rev. B 46, 13643 (1992)
P.B. Allen: Empirical electron-phonon λ values from resistivity of cubic metallic elements, Phys. Rev. B 36, 2920(1987)
A. Bartholmei, P. Fouquet, G. Witte: Growth and dynamics of ultrathin barium films on Cu(100), Surf. Sci. 473, 227 (2001)
G. Benedek, J.R. Manson, S. Miret-Artès: The electron–phonon interaction of low-dimensional and multi-dimensional materials from he atom scattering, Advanced Materials 32, 2002072 (2020)
I.Y. Sklyadneva, R. Heid, K.-P. Bohnen, P.M. Echenique, G. Benedek, E.V. Chulkov: The effect of spin–orbit coupling on the surface dynamical properties and electron–phonon interaction of Tl(0001), J. Phys. Chem. A 115, 7352 (2011)
I.Y. Sklyadneva, R. Heid, K.-P. Bohnen, P.M. Echenique, E.V. Chulkov: Surface phonons on Pb(111), J. Phys. Condens. Matter 24, 104004 (2012)
J. Braun, P. Ruggerone, G. Zhang, J.P. Toennies, G. Benedek: Surface phonon dispersion curves of thin Pb films on Cu(111), Phys. Rev. B 79, 205423 (2009)
G.G. Rusina, S.D. Borisova, S.V. Eremeev, I.Y. Sklyadneva, E.V. Chulkov, G. Benedek, J.P. Toennies: Surface dynamics of the wetting layers and ultrathin films on a dynamic substrate: (0.5–4) ML Pb/Cu(111), J. Phys. Chem. C 120, 22304 (2016)
F. Calleja, A.L. Vázquez de Parga, E. Anglada, J.J. Hinarejos, R. Miranda, F. Yndurain: Crystallographic and electronic contribution to the apparent step height in nanometer-thin Pb(111) films grown on Cu(111), New J. Phys. 11, 123003(2009)
23.356 A. Tamtögl, P. Kraus, M. Mayrhofer-Reinhartshuber, W.E. Ernst, D. Campi, M. Bernasconi,G. Benedek: Surface and subsurface phonons of Bi(111) measured with helium atom scattering, Phys. Rev. B 87, 035410 (2013)
V. Chis, G. Benedek, P.M. Echenique, E.V. Chulkov: Phonons in ultrathin Bi(111) films: role of spinorbit coupling in electron–phonon interaction, Phys. Rev. 87, 075412 (2013)
P. Kraus, A. Tamtögl, M. Mayrhofer-Reinhartshuber, G. Benedek, W.E. Ernst: Resonance-enhanced inelastic He-atom scattering from subsurface optical phonons of Bi(111), Phys. Rev. B 87, 245433 (2013)
P. Hofmann: The surfaces of bismuth: Structural and electronic properties, Prog. Surf. Sci. 81, 191 (2006)
G.Q. Huang, J. Yang: Surface lattice dynamics and electron–phonon interaction in ultrathin Bi(111) film, J. Phys. Condens. Matter 25, 175004 (2013)
M. Alcántara Ortigoza, I.Y. Sklyadneva, R. Heid, E.V. Chulkov, T.S. Rahman, K.-P. Bohnen, P.M. Echenique: Ab initio lattice dynamics and electron–phonon coupling of Bi(111), Phys. Rev. B 90, 195438(2014)
M. Verstraete, G. Benedek: Lattice dynamics of polonium: symmetry breaking phase transitions and surface phonons. In: Mater. Res. Soc. Symp. Proc. Ser, Vol. 1404E (2011), Paper W1.11
A. Khater, R. Tigrine, B. Bourahla: Polonium bulk and surface vibrational dynamics, Phys. Status Solidi (b) 246, 1614 (2009)
M.J. Verstraete: Phases of polonium via density functional theory, Phys. Rev. Lett. 104, 035501 (2010)
D.A. Papaconstantopoulos: Handbook of the Band Structure of Elemental Solids: From Z = 1 to Z =112, 2nd edn. (Springer, Berlin, Heidelberg 2015) pp. 400–427
A. Hermann, R. Hofmann, N. Ashcroft: Condensed astatine: monatomic and metallic, Phys. Rev. Lett. 111, 116404 (2013)
R. Eichler, M. Schädel: Adsorption of radon on metal surfaces: a model study for chemical investigations of elements 112 and 114, J. Phys. Chem. B 106, 5413(2002)
M. Magomedov: The calculation of the parameters of the Mie–Lennard-Jones potential, High Temp. 44, 513 (2006)
K.T. Tang, J.P. Toennies: The van der Waals potentials between all the rare gas atoms from He to Rn, J. Chem. Phys. 118, 4976(2003)
D. Campi: Atomistic simulation of thermal transport and vibrational properties in phase change materials, Dissertation (University Milano-Bicocca, Milan 2015)
A. Ruckhofer, D. Campi, M. Bremholm, Ph Hofmann, G. Benedek, M. Bernasconi, W.E. Ernst, A. Tamtögl: THz surface excitations and electronphonon coupling in Bi2 Se3 (111) from helium atom scattering, Phys. Rev. Res. 2, 023186 (2020)
D. Campi, M. Bernasconi, G. Benedek: Ab-initio calculation of surface phonons at the Sb2Te3 (111) surface, Surf. Sci. 678, 46–51 (2018)
K.M.F. Shahil, M.Z. Hossain, V. Goyal, A.A. Balandin: Micro-Raman spectroscopy of mechanically exfoliated few-quintuple layers of Bi2 Te3, Bi2 Se3,andSb2 Te3 materials, J. Appl. Phys. 111, 054305 (2012)
A. Tamtögl, D. Campi, M. Bremholm, E.M.J. Hedegaard, B.B. Iversen, M. Bianchi, P. Hofmann, N. Marzari, G. Benedek, J. Ellis, W. Allison: Surface phonon dispersion of Bi2 Te3 (111): evidence for a prominent surface acoustic wave and the role of van der Waals Interactions, arXiv:1803.11184v1 [cond-mat.mtrl-sci] (2018)
A. Tamtögl, D. Campi, M. Bremholm, E.M.J. Hedegaard, B.B. Iversen, M. Bianchi, P. Hofmann, N. Marzari, G. Benedek, J. Ellis, W. Allison: Nanoscale surface dynamics of Bi2 Te3 (111): observation of a prominent surface acoustic wave and the role of van der Waals interactions, Nanoscale 10(30), 14627–14636 (2018)
C. Howard, M. El-Batanouny: Connecting electron and phonon spectroscopy data to consistently determine quasiparticle-phonon coupling on the surface of topological insulators, Phys. Rev. B 89, 075425 (2014)
C. Howard, M. El-Batanouny, R. Sankar, F.C. Chou: Anomalous behavior in the phonon dispersion of the (001) surface of Bi2 Te3 determined from helium atom-surface scattering measurements, Phys.Rev.B88, 035402 (2013)
S.V. Eremeev, M.G. Vergniory, T.V. Menshchikova, A.A. Shaposhnikov, E.V. Chulkov: The effect of van der Waal’s gap expansions on the surface electronic structure of layered topological insulators, New J. Phys. 14, 113030 (2012)
M. Wiesner, A. Trzaskowska, B. Mroz, S. Charpentier, S. Wang, Y. Song, F. Lombardi, P. Lucignano, D. Campi, M. Bernasconi, G. Benedek, F. Guinea, A. Tagliacozzo: The electron–phonon interaction at deep Bi2 Te3-semiconductor interfaces from Brillouin light scattering, Sci. Rep. 7, 16449 (2017)
R. Heid, I.Y. Sklyadneva, E.V. Chulkov: Electronphonon coupling in topological surface states: The role of polar optical modes, Sci. Rep. 7, 1095 (2017)
C. Bungaro, S. de Gironcoli, S. Baroni: Theory of the anomalous Rayleigh dispersion at H/W(110) surfaces, Phys. Rev. Lett. 77, 2491(1996)
J. Lüdecke: Vergleichende Untersuchung der sauberen und adsorbatbedeckten W(110) und Mo(110)-Oberfläche mit hoch auflösender Helium-Atomstrahlstreuung, Bericht 15 (MaxPlanck-Institut für Strömungsforschung, Göttingen 1984)
23.383 E. Hulpke, J. Lüdecke: Vibrational properties of the clean W(110) surface and of different hydrogen adsorbate phases studied by helium atom scattering, Surf. Sci. 272, 289 (1992)
E. Hulpke, J. Lüdecke: The giant surface phonon anomaly on hydrogen saturated W(110) and Mo(110), Surf. Sci. 287/288, 837 (1993)
E. Hulpke, J. Lüdecke: Surface phonon anomaly induced by adsorption, J. Electron Spectrosc. Relat. Phenom. 64/65, 641 (1993)
M. Balden, S. Lehwald, E. Preuss, H. Ibach: Surface phonons of the clean and H-covered W(110) surface measured with EELS, Surf. Sci. 309, 1141 (1994)
M. Balden, S. Lehwald, H. Ibach, D.L. Mills: Hydrogen covered W(110) surface: a hydrogen liquid with a propensity for one-dimensional order, Phys.Rev.Lett.73, 854(1994)
G. Benedek, M. Pardo, J.P. Toennies: Theory of inelastic atom scattering from surface electron– hole and plasmon excitations. In: Highlights on Spectroscopies of Semiconductors and Nanostructures, Conf. Proc., Vol. 94, ed. by G. Guizzetti, A.C. Andreani, F. Marabelli, M. Patrini (SIF, Bologna 2007) pp. 151–167
B. Kohler, P. Ruggerone, M. Scheffler, E. Tosatti: Enhanced electron–phonon coupling at the Mo and W(110) surfaces induced by adsorbed hydrogen, Z. Phys. Chem. 197, 193 (1996)
B. Kohler, P. Ruggerone, M. Scheffler: Anomalies in He atom scattering spectra of the H-covered Mo(110) and W(110) surfaces, Surf. Sci. 368, 213 (1996)